Question 310928
Basic fact:

The altitude of an equilateral triangle bisects the side on which it stands and forms right angled triangles with the remaining sides.

It would have been better if I could have drawn this here but as I cant I will try to explain it in words.

We have the length of each side = 12cm
Therefore the altitude bisects the side on which it stands into 2 equals each measuring 6cm
Hence one half of the triangle being a right angled triangle will have the following measurements

Hypotenus = side of the triangle = 12cm
Base= half of the side on which the altitude stands = 6 cm

Therefore as per the Pythagoras theorem

{{{Altitude ^2 = Hypotenuse^2 - Base^2}}}
= {{{12^2 - 6^2}}}
= {{{144 - 36}}}
= {{{108}}}

Therefor the Altitude = {{{(108)^(1/2)}}}
= {{{6^(1/3)}}}